Let's solve each problem step by step and explain the reasoning behind the solutions. The problems involve finding
perimeter and
area of rectangles, using formulas:
-
Perimeter (P) of a rectangle:
$ P = 2 \times (\text{length} + \text{width}) $
-
Area (A) of a rectangle:
$ A = \text{length} \times \text{width} $
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1) A rug had a length of 9 feet and a width of 3 feet. What is the perimeter of the rug?
- Length = 9 ft, Width = 3 ft
- $ P = 2 \times (9 + 3) = 2 \times 12 = 24 $ ft
✔ Answer: 24 ft
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2) A piece of plywood was cut so its length was 6 feet by 2 feet. What is the area of the wood?
- Length = 6 ft, Width = 2 ft
- $ A = 6 \times 2 = 12 $ ft²
✔ Answer: 12 ft²
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3) Rachel had a sheet of paper that was 9 inches long and 4 inches wide. What is the perimeter of the paper?
- Length = 9 in, Width = 4 in
- $ P = 2 \times (9 + 4) = 2 \times 13 = 26 $ in
✔ Answer: 26 in
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4) Carol was cutting out some fabric for a friend. She cut a piece that was 6 centimeters wide and had an area of 30 cm². How long was the piece?
- Area = 30 cm², Width = 6 cm
- Use: $ \text{Area} = \text{length} \times \text{width} $
- So: $ \text{length} = \frac{\text{Area}}{\text{width}} = \frac{30}{6} = 5 $ cm
✔ Answer: 5 cm
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5) Tiffany had a sheet of paper that was 9 inches long and the area was 63 in². What is the width of the paper?
- Area = 63 in², Length = 9 in
- $ \text{width} = \frac{\text{Area}}{\text{length}} = \frac{63}{9} = 7 $ in
✔ Answer: 7 in
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6) The woods behind Tom's house were 6 miles wide and 10 miles long. What is the area of the woods?
- Width = 6 mi, Length = 10 mi
- $ A = 6 \times 10 = 60 $ mi²
✔ Answer: 60 mi²
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7) Lana was cutting out some fabric for a friend. She cut a piece that was 7 centimeters wide and 6 centimeters long. What is the area of the fabric she cut out?
- Width = 7 cm, Length = 6 cm
- $ A = 7 \times 6 = 42 $ cm²
✔ Answer: 42 cm²
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8) An island in the Indian Ocean was 4 miles wide and 10 miles long. What is the perimeter of the island?
- Width = 4 mi, Length = 10 mi
- $ P = 2 \times (10 + 4) = 2 \times 14 = 28 $ mi
✔ Answer: 28 mi
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9) The woods behind Victor's house were 5 miles wide and 6 miles long. What is the perimeter of the woods?
- Width = 5 mi, Length = 6 mi
- $ P = 2 \times (5 + 6) = 2 \times 11 = 22 $ mi
✔ Answer: 22 mi
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10) A bathroom had a length of 2 feet and a total area of 6 ft². What is the width of the bathroom?
- Area = 6 ft², Length = 2 ft
- $ \text{width} = \frac{\text{Area}}{\text{length}} = \frac{6}{2} = 3 $ ft
✔ Answer: 3 ft
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✔ Final Answers:
1. 24 ft
2. 12 ft²
3. 26 in
4. 5 cm
5. 7 in
6. 60 mi²
7. 42 cm²
8. 28 mi
9. 22 mi
10. 3 ft
These match the answer key provided.
Let me know if you'd like a visual explanation or practice problems!
Parent Tip: Review the logic above to help your child master the concept of perimeter and area worksheet 6th grade.
